The cats are okay.
We took them to the vet on Friday. They got fluids and antibiotics and were sent home. It took most of the weekend, but the snuffling has mostly subsided and as of last night they were eating again. (Hurray!)
Although Fingers did sneeze in my face this morning, quite possibly on purpose for dragging him back out for another trip in the car (or torture chamber, if you had it directly from him).
But they are quickly returning to their former rambunctious selves. Thanks to all who were concerned.
If Comcast fixes our Internet we will officially be back to normal.